Leo Varadkar says himself and the Foreign Affairs Minister have accepted they didn't handle her appointment to a now defunct UN role properly.
The Tanaiste has apologised for not publishing text messages of the appointment sooner while Simon Coveney says he deleted his texts over hacking concerns.
The Foreign Affairs Minister says his phone was used to contact some of his fellow EU counterparts after it was hacked last year.
Simon Coveney says the matter was dealt with swiftly and the hack led to him being more careful about the security of his texts.
The Chairman of the Foreign Affairs Committee said he still had questions to answer over his deleted messages about the Katherine Zappone UN appointment.
Minister Coveney's written to Charlie Flanagan to insist any suggestion he was trying to keep his texts to the Tanaiste secret are "plain wrong".
Speaking earlier, Leo Varadkar said he believes he still has the support of his Government colleagues.